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Kirchhoff’s laws

10.2

What the syllabus asks of you

  • recall Kirchhoff’s first law and understand that it is a consequence of conservation of charge
  • recall Kirchhoff’s second law and understand that it is a consequence of conservation of energy
  • derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in series
  • use the formula for the combined resistance of two or more resistors in series
  • derive, using Kirchhoff’s laws, a formula for the combined resistance of two or more resistors in parallel
  • use the formula for the combined resistance of two or more resistors in parallel
  • use Kirchhoff’s laws to solve simple circuit problems

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Chapter 10: Kirchhoff's laws

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113 questions

1May / June 2026 · Paper 11 · Q35
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A
B
C
D

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2May / June 2026 · Paper 12 · Q36
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Acharge / energy
Benergy / current
Ccurrent / charge
Denergy / charge

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3May / June 2026 · Paper 12 · Q37
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A125 Ω
B167 Ω
C250 Ω
D500 Ω

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4May / June 2026 · Paper 13 · Q36
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AX → Z → Y
BY → X → Z
CY → Z → X
DZ → Y → X

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5May / June 2026 · Paper 14 · Q35
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A20 Ω
B30 Ω
C32 Ω
D36 Ω

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6May / June 2026 · Paper 14 · Q37
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A0.17 A
B0.25 A
C0.33 A
D1.3 A

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7Oct / Nov 2025 · Paper 11 · Q34
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A0.40 Ω
B0.80 Ω
C2.0 Ω
D2.8 Ω

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8Oct / Nov 2025 · Paper 11 · Q37
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AI1 = I2 + I4 + I5
BI2 = I1 – I3
CI2 = I3 + I4 + I5
DI4 = I3 – I5

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9Oct / Nov 2025 · Paper 12 · Q37
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Afirst law: charge; second law: energy
Bfirst law: charge; second law: voltage
Cfirst law: energy; second law: charge
Dfirst law: voltage; second law: charge

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10Oct / Nov 2025 · Paper 13 · Q34
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A0.40 Ω
B0.80 Ω
C2.0 Ω
D2.8 Ω

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11Oct / Nov 2025 · Paper 13 · Q37
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AI1 = I2 + I4 + I5
BI2 = I1 – I3
CI2 = I3 + I4 + I5
DI4 = I3 – I5

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12Oct / Nov 2025 · Paper 14 · Q36
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A2 V
B4 V
C6 V
D10 V

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13May / June 2025 · Paper 11 · Q34
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APQ
BQR
CRS
DSP

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14May / June 2025 · Paper 11 · Q36
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AR1 + R2
B\frac{R_1 R_2}{R_1 + R_2}
C\frac{R_1 + R_2}{R_1 R_2}
D\frac{R_1}{R_2}

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15May / June 2025 · Paper 12 · Q36
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ACircuit A: terminals 1 and 3 connected via resistors to 2 and 4 respectively, with 2-4 connected by a wire
BCircuit B: terminals 1 and 3 connected via resistors to 2 and 4 respectively, with 1-3 and 2-4 connected by wires
CCircuit C: terminal 1 connected via resistor to 2, 3 connected via resistor to 1, and 2-4 connected by a wire
DCircuit D: terminal 1 connected via resistor to 3, and 2-4 connected by a wire

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16May / June 2025 · Paper 12 · Q37
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AThe algebraic sum of currents at a junction is zero. / charge
BThe algebraic sum of currents at a junction is zero. / energy
CThe e.m.f. in a loop is equal to the algebraic sum of the product of current and resistance round the loop. / charge
DThe e.m.f. in a loop is equal to the algebraic sum of the product of current and resistance round the loop. / energy

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17May / June 2025 · Paper 14 · Q33
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ACircuit A
BCircuit B
CCircuit C
DCircuit D

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18May / June 2025 · Paper 14 · Q34
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AThis is Kirchhoff's first law, which results from the conservation of charge.
BThis is Kirchhoff's first law, which results from the conservation of energy.
CThis is Kirchhoff's second law, which results from the conservation of charge.
DThis is Kirchhoff's second law, which results from the conservation of energy.

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19May / June 2025 · Paper 14 · Q35
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A12 Ω
B30 Ω
C50 Ω
D60 Ω

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20Oct / Nov 2024 · Paper 11 · Q31
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AThe charge flowing in an electric circuit is conserved.
BThe energy in an electric circuit is conserved.
CThe sum of the electric currents entering a point in an electric circuit is equal to the sum of the electric currents leaving that point.
DThe sum of the potential differences in an electric circuit is equal to the sum of the products of the current and resistance.

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21Oct / Nov 2024 · Paper 11 · Q36
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A
B
C
D

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22Oct / Nov 2024 · Paper 12 · Q35
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ACircuit A: 100 Ω and 100 Ω in parallel, in series with 50 Ω
BCircuit B: 50 Ω and 100 Ω in parallel, in series with 100 Ω
CCircuit C: 100 Ω, 100 Ω and 50 Ω in parallel
DCircuit D: 100 Ω, 100 Ω and 50 Ω in series

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23Oct / Nov 2024 · Paper 12 · Q36
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Afirst law: charge; second law: energy
Bfirst law: energy; second law: current
Cfirst law: power; second law: charge
Dfirst law: resistance; second law: power

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24May / June 2024 · Paper 11 · Q34
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A30 Ω
B90 Ω
C160 Ω
D480 Ω

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25May / June 2024 · Paper 11 · Q36
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ART = R1 + R2 + R3
BRT = 1/(R1 + R2) + 1/R3
C1/RT = 1/(R1 + R2 + R3)
D1/RT = 1/(R1 + R2) + 1/R3

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26May / June 2024 · Paper 12 · Q30
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Areading on X / A: 4.0, reading on Y / A: 1.3
Breading on X / A: 4.0, reading on Y / A: 2.7
Creading on X / A: 6.0, reading on Y / A: 2.0
Dreading on X / A: 6.0, reading on Y / A: 4.0

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27May / June 2024 · Paper 12 · Q34
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AIt considers the currents at a junction in a circuit and is a consequence of the conservation of charge.
BIt considers the currents at a junction in a circuit and is a consequence of the conservation of energy.
CIt considers the electromotive forces and potential differences in a circuit loop and is a consequence of the conservation of charge.
DIt considers the electromotive forces and potential differences in a circuit loop and is a consequence of the conservation of energy.

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28May / June 2024 · Paper 12 · Q35
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AIt is between r and R.
BIt is equal to (r + R).
CIt is greater than (r + R).
DIt is less than r.

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29May / June 2024 · Paper 13 · Q32
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AA
BB
CC
DD

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30May / June 2024 · Paper 13 · Q34
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A20 and 40, parallel
B40 and 100, parallel
C20 and 40, series
D40 and 100, series

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31May / June 2024 · Paper 13 · Q36
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A1.5 Ω
B2.5 Ω
C3.5 Ω
D5.0 Ω

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32Feb / March 2024 · Paper 12 · Q33
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A0.67 kΩ
B1.6 kΩ
C3.2 kΩ
D8.1 kΩ

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33Oct / Nov 2023 · Paper 11 · Q31
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A0.50 Ω
B1.0 Ω
C1.5 Ω
D2.3 Ω

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34Oct / Nov 2023 · Paper 11 · Q35
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Acharge and energy
Bcharge and resistance
Cmass and energy
Dmass and resistance

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35Oct / Nov 2023 · Paper 12 · Q35
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Acharge
Benergy
Clinear momentum
Dpotential difference

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36Oct / Nov 2023 · Paper 12 · Q36
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A3.0 Ω
B5.0 Ω
C7.2 Ω
D18 Ω

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37Oct / Nov 2023 · Paper 13 · Q35
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AI₀ = I₁ = I₂ = I₃
BI₀ = I₁ + I₂ + I₃
CV₀ = V₁ = V₂ = V₃
DV₀ = V₁ + V₂ + V₃

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38Oct / Nov 2023 · Paper 13 · Q36
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A2.7 Ω
B4.0 Ω
C5.3 Ω
D12 Ω

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39May / June 2023 · Paper 12 · Q35
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Acharge
Benergy
Cmomentum
Dpotential difference

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40May / June 2023 · Paper 12 · Q36
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A0
B\frac{E}{3}
C\frac{2E}{3}
DE

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41May / June 2023 · Paper 13 · Q31
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A0.50 Ω
B2.7 Ω
C4.0 Ω
D6.0 Ω

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42May / June 2023 · Paper 13 · Q35
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Acharge
Benergy
Cmass
Dmomentum

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43May / June 2023 · Paper 13 · Q36
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A15 Ω
B17 Ω
C23 Ω
D27 Ω

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44Feb / March 2023 · Paper 12 · Q35
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Acharge; current
Bcharge; energy
Ccurrent; mass
Denergy; current

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45Oct / Nov 2022 · Paper 11 · Q34
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Alamp P brighter, lamp R brighter
Blamp P brighter, lamp R dimmer
Clamp P dimmer, lamp R brighter
Dlamp P dimmer, lamp R dimmer

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46Oct / Nov 2022 · Paper 13 · Q35
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Aenergy; charge
Benergy; momentum
Ccharge; energy
Dmomentum; energy

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47Oct / Nov 2022 · Paper 13 · Q36
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A1.5 V
B2.1 V
C7.1 V
D12.1 V

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48May / June 2022 · Paper 11 · Q36
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AIt is a consequence of the conservation of charge.
BIt is a consequence of the conservation of electromotive force.
CIt is a consequence of the conservation of energy.
DIt is a consequence of the conservation of potential difference.

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49May / June 2022 · Paper 12 · Q36
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Afirst law: charge; second law: energy
Bfirst law: energy; second law: current
Cfirst law: current; second law: charge
Dfirst law: energy; second law: charge

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50May / June 2022 · Paper 13 · Q37
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AKirchhoff's first law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. physics principle applied for first law: conservation of charge. Kirchhoff's second law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. physics principle applied for second law: conservation of energy
BKirchhoff's first law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. physics principle applied for first law: conservation of energy. Kirchhoff's second law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. physics principle applied for second law: conservation of charge
CKirchhoff's first law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. physics principle applied for first law: conservation of energy. Kirchhoff's second law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. physics principle applied for second law: conservation of charge
DKirchhoff's first law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. physics principle applied for first law: conservation of charge. Kirchhoff's second law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. physics principle applied for second law: conservation of energy

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51Feb / March 2022 · Paper 12 · Q35
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Athe algebraic sum of currents into a junction is zero — charge
Bthe algebraic sum of currents into a junction is zero — energy
Cthe e.m.f. in a loop is equal to the algebraic sum of the product of current and resistance round the loop — charge
Dthe e.m.f. in a loop is equal to the algebraic sum of the product of current and resistance round the loop — energy

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52Feb / March 2022 · Paper 12 · Q36
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A0.50 Ω
B2.0 Ω
C4.0 Ω
D8.0 Ω

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53Oct / Nov 2021 · Paper 12 · Q37
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Acurrent 0.1 A, e.m.f. 4 V
Bcurrent 0.3 A, e.m.f. 4 V
Ccurrent 0.1 A, e.m.f. 6 V
Dcurrent 0.3 A, e.m.f. 6 V

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54Oct / Nov 2021 · Paper 13 · Q36
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A4/5
B5/4
C1/2
D2/1

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55Oct / Nov 2021 · Paper 13 · Q37
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A0.20 A
B0.60 A
C1.0 A
D1.8 A

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56May / June 2021 · Paper 11 · Q36
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A\frac{R}{6}
B\frac{6R}{11}
C\frac{11R}{6}
D6R

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57May / June 2021 · Paper 12 · Q37
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AI₁ = I₂ + I₃
BI₁ = I₂ = I₃
CE = V₁ + V₂
DV₁ = V₂ = V₃

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58May / June 2021 · Paper 13 · Q35
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A2.7 A
B4.0 A
C8.0 A
D13 A

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59May / June 2021 · Paper 13 · Q37
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A0 = I1(R1 + R2) + I2(R3 + R4)
B0 = I1(R1 + R2) – I2(R3 + R4)
CE = I1(R1 + R2) + I2(R3 + R4)
DE = I1(R1 + R2) – I2(R3 + R4)

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60Feb / March 2021 · Paper 12 · Q33
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Apower dissipated in R1 = power dissipated in R2 + power dissipated in R3
Bpower dissipated in R2 = power dissipated in R3
Cpower output of cell = power dissipated in R1 + power dissipated in R2 + power dissipated in R3
Dpower output of cell = power dissipated in R1

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61Oct / Nov 2020 · Paper 11 · Q36
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Abrighter brighter
Bbrighter dimmer
Cdimmer brighter
Ddimmer dimmer

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62Oct / Nov 2020 · Paper 11 · Q37
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A20 μA
B30 μA
C40 μA
D60 μA

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63Oct / Nov 2020 · Paper 13 · Q37
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A6.0 V
B15 V
C20 V
D24 V

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64May / June 2020 · Paper 11 · Q37
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A3.0 Ω
B6.0 Ω
C12 Ω
D18 Ω

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65May / June 2020 · Paper 12 · Q37
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Afirst law: charge; second law: energy
Bfirst law: charge; second law: momentum
Cfirst law: energy; second law: charge
Dfirst law: energy; second law: momentum

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66May / June 2020 · Paper 13 · Q35
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A15 V
B29 V
C39 V
D51 V

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67Feb / March 2020 · Paper 12 · Q33
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A1/3
B4/3
C2/1
D3/1

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68Oct / Nov 2019 · Paper 11 · Q34
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Acharge / current
Bcharge / energy
Ccurrent / mass
Denergy / current

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69Oct / Nov 2019 · Paper 11 · Q36
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AV1 = V2 + V4
BV1 = V2 + V3 + V4
CV2 + V3 = V4
DV3 + V4 – V2 = 0

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70Oct / Nov 2019 · Paper 11 · Q37
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A0.17 A
B0.25 A
C0.33 A
D1.3 A

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71Oct / Nov 2019 · Paper 11 · Q38
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AA₂ = 1.0 A, A₃ = 0.3 A, A₄ = 0.1 A
BA₂ = 1.4 A, A₃ = 0.6 A, A₄ = 0.2 A
CA₂ = 1.8 A, A₃ = 0.9 A, A₄ = 0.3 A
DA₂ = 2.2 A, A₃ = 1.2 A, A₄ = 0.4 A

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72Oct / Nov 2019 · Paper 12 · Q36
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AX → Y → Z
BX → Z → Y
CY → X → Z
DY → Z → X

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73Oct / Nov 2019 · Paper 13 · Q34
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A2.7 W
B6.0 W
C11 W
D24 W

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74Oct / Nov 2019 · Paper 13 · Q37
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AKirchhoff's first law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. | physics principle applied for first law: conservation of charge | Kirchhoff's second law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. | physics principle applied for second law: conservation of energy
BKirchhoff's first law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. | physics principle applied for first law: conservation of energy | Kirchhoff's second law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. | physics principle applied for second law: conservation of charge
CKirchhoff's first law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. | physics principle applied for first law: conservation of energy | Kirchhoff's second law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. | physics principle applied for second law: conservation of charge
DKirchhoff's first law: The sum of the e.m.f.s around any closed loop in a circuit equals the sum of the p.d.s around the same loop. | physics principle applied for first law: conservation of charge | Kirchhoff's second law: The sum of the currents entering a junction equals the sum of the currents leaving the junction. | physics principle applied for second law: conservation of energy

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75Oct / Nov 2019 · Paper 13 · Q38
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AV3 = 1.5 V, V4 = 1.0 V
BV3 = 3.0 V, V4 = 2.0 V
CV3 = 4.5 V, V4 = 3.0 V
DV3 = 6.0 V, V4 = 4.0 V

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76May / June 2019 · Paper 11 · Q37
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A0.10 A
B0.15 A
C0.20 A
D0.30 A

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77May / June 2019 · Paper 12 · Q36
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Acharge
Benergy
Cmass
Dmomentum

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78May / June 2019 · Paper 13 · Q36
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AAll three lamps light with normal brightness.
BOnly lamp 2 lights with normal brightness.
COnly lamps 1 and 3 light with normal brightness.
DNone of the lamps light with normal brightness.

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79May / June 2019 · Paper 13 · Q38
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A0.10 A
B0.20 A
C0.30 A
D0.47 A

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80Feb / March 2019 · Paper 12 · Q37
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AP → S → Q → R
BP → S → R → Q
CQ → R → S → P
DS → P → Q → R

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81Oct / Nov 2018 · Paper 11 · Q37
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A4.4 V
B4.6 V
C6.6 V
D11.2 V

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82Oct / Nov 2018 · Paper 12 · Q36
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Alargest current: PQ; smallest current: PR
Blargest current: PQ; smallest current: QS
Clargest current: RS; smallest current: PR
Dlargest current: RS; smallest current: QS

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83Oct / Nov 2018 · Paper 12 · Q37
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AThe charge flowing in an electric circuit is conserved.
BThe energy in an electric circuit is conserved.
CThe sum of the electric currents entering a point in an electrical circuit is equal to the sum of the electric currents leaving that point.
DThe sum of the potential differences in a circuit is equal to the sum of the products of the current and resistance.

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84Oct / Nov 2018 · Paper 13 · Q33
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A24 V
B30 V
C40 V
D60 V

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85Oct / Nov 2018 · Paper 13 · Q36
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AW → Z → Y → X
BX → W → Y → Z
CX → Y → W → Z
DX → Y → Z → W

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86May / June 2018 · Paper 11 · Q33
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AThis is Kirchhoff's first law, which results from the conservation of charge.
BThis is Kirchhoff's first law, which results from the conservation of energy.
CThis is Kirchhoff's second law, which results from the conservation of charge.
DThis is Kirchhoff's second law, which results from the conservation of energy.

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87May / June 2018 · Paper 11 · Q34
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A$I_1 = -5.5\,\text{A}$, $I_2 = 1.0\,\text{A}$, $I_3 = 6.5\,\text{A}$
B$I_1 = 0.5\,\text{A}$, $I_2 = 4.0\,\text{A}$, $I_3 = 3.5\,\text{A}$
C$I_1 = 3.5\,\text{A}$, $I_2 = 4.0\,\text{A}$, $I_3 = 0.5\,\text{A}$
D$I_1 = 6.5\,\text{A}$, $I_2 = 1.0\,\text{A}$, $I_3 = -5.5\,\text{A}$

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88May / June 2018 · Paper 11 · Q35
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A0.25 mA
B0.50 mA
C0.75 mA
D1.0 mA

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89May / June 2018 · Paper 12 · Q34
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A0.21 A
B0.50 A
C0.75 A
D1.0 A

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90May / June 2018 · Paper 12 · Q36
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ACircuit A
BCircuit B
CCircuit C
DCircuit D

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91May / June 2018 · Paper 13 · Q34
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ACircuit A: 6.0 V battery connected to one 6.0 Ω resistor in series with a parallel combination of two 6.0 Ω resistors.
BCircuit B: 6.0 V battery connected to three 6.0 Ω resistors in series.
CCircuit C: 6.0 V battery connected to a parallel combination of two 6.0 Ω resistors in series with a third 6.0 Ω resistor.
DCircuit D: 6.0 V battery connected to three 6.0 Ω resistors in parallel.

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92May / June 2018 · Paper 13 · Q35
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A0.30 Ω
B0.53 Ω
C1.9 Ω
D3.3 Ω

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93May / June 2018 · Paper 13 · Q36
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Adecrease, decrease
Bdecrease, increase
Cincrease, decrease
Dincrease, increase

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94Feb / March 2018 · Paper 12 · Q38
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A0.25 Ω
B0.61 Ω
C4.0 Ω
D16 Ω

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95Oct / Nov 2017 · Paper 11 · Q36
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AI decreases, V decreases
BI increases, V increases
CI increases, V stays the same
DI stays the same, V increases

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96Oct / Nov 2017 · Paper 11 · Q37
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AI1R1 + I2R2 = I3R3 + I3R4
BI2R2 – I3R4 – I3R3 = 0
CE = I1R1 + I2R2 + I3R3 + I3R4
DE = I1R1 + I2R2 – I3R3 – I3R4

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97Oct / Nov 2017 · Paper 12 · Q34
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Apower loss in R$_1$ = power loss in R$_2$ + power loss in R$_3$
Bpower loss in R$_2$ = power loss in R$_3$
Cpower output of cell = power loss in R$_1$ + power loss in R$_2$ + power loss in R$_3$
Dpower output of cell = power loss in R$_1$

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98Oct / Nov 2017 · Paper 12 · Q37
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A3.0 Ω
B4.0 Ω
C4.8 Ω
D5.0 Ω

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99Oct / Nov 2017 · Paper 13 · Q37
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A0
B\frac{E}{3}
C\frac{2E}{3}
DE

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100Oct / Nov 2017 · Paper 13 · Q38
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A1 Ω and 2 Ω in series with ammeter between P and Q
B1 Ω and 2 Ω in parallel with ammeter between P and Q
C1 Ω in series with ammeter, in parallel with 2 Ω between P and Q
D1 Ω and 2 Ω in parallel with ammeter in the middle branch between P and Q

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101May / June 2017 · Paper 11 · Q37
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A1 Ω in series with a parallel combination of 2 Ω and 3 Ω
B2 Ω in series with a parallel combination of 1 Ω and 3 Ω
C1 Ω and 2 Ω in series, in parallel with 3 Ω
D1 Ω, 2 Ω and 3 Ω in parallel

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102May / June 2017 · Paper 12 · Q36
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AP and Q
BQ and S
CR and S
DS and P

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103May / June 2017 · Paper 13 · Q35
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Apotential drop across M / V: 9; potential drop across P / V: 7; potential drop across Q / V: 13
Bpotential drop across M / V: 13; potential drop across P / V: 7; potential drop across Q / V: 13
Cpotential drop across M / V: 13; potential drop across P / V: 11; potential drop across Q / V: 9
Dpotential drop across M / V: 17; potential drop across P / V: 3; potential drop across Q / V: 17

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104Feb / March 2017 · Paper 12 · Q36
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A11 kΩ
B18 kΩ
C22 kΩ
D36 kΩ

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105Oct / Nov 2016 · Paper 11 · Q37
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AI1 = I2 + I3
BI2 = I1 + I3
CI3 = I4 + I5
DI4 = I5 + I3

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106Oct / Nov 2016 · Paper 12 · Q37
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AI / A: 3.0; V / V: 10.5
BI / A: 4.0; V / V: 9.0
CI / A: 4.0; V / V: 12
DI / A: 12; V / V: 18

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107Oct / Nov 2016 · Paper 13 · Q37
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AI1 = I2 + I3
BI2 = I1 + I3
CI3 = I4 + I5
DI4 = I5 + I3

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108May / June 2016 · Paper 11 · Q35
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A2 V, 4 V
B2 V, 10 V
C3 V, 4 V
D3 V, 10 V

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109May / June 2016 · Paper 11 · Q36
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AR1 + R2
B\frac{R_1 R_2}{R_1 + R_2}
C\frac{R_1 + R_2}{R_1 R_2}
D\frac{R_1}{R_2}

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110May / June 2016 · Paper 13 · Q35
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Adecreases / decreases
Bdecreases / increases
Cincreases / decreases
Dincreases / increases

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111Feb / March 2016 · Paper 12 · Q34
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A$V_1 + V_2 + V_3 = I(R_1 + R_2 + R_3)$
B$V_1 + V_2 - V_3 = I(R_1 + R_2 + R_3)$
C$V_1 - V_2 + V_3 = I(R_1 + R_2 + R_3)$
D$V_1 - V_2 - V_3 = I(R_1 + R_2 + R_3)$

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112Feb / March 2016 · Paper 12 · Q35
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A$2.7\,\Omega$
B$4.0\,\Omega$
C$5.3\,\Omega$
D$12\,\Omega$

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113Feb / March 2016 · Paper 12 · Q36
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Athe conservation of charge
Bthe direction of the flow of charge is from negative to positive
Cthe potential difference across each resistor is the same
Dthe current varies in each resistor, in proportion to the resistor value

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